The layered cobaltites provide fascinating platform for exploring functional properties of oxides
both in fundamental and applicational viewpoints [1]}.
Since the discovery of large thermopower in the metallic Na\(_x\) CoO\(_2\)  [2]},
this class of materials has been recognized as potential oxide thermoelectrics
that possesses a high-temperature stability in air [3]}, [4]}, [5]}.
The crystal structure of this family is composed of
two subsystems of an insulating layer and
CdI\(_2\) -type CoO\(_2\)  conduction layer
alternately stacked
along the \(c\)  axis.
As for the origin of the large thermopower coexisting with the metallic conductivity,
Koshibae et al. have suggested a localized model in which
a hopping conduction of correlated \(d\)  electrons
with spin and orbital degeneracies involves large entropy flow [6]}.
This picture is supported by magnetic field dependence of the thermopower [7]} and
is also discussed in semiconducting cobalt oxides [8]}.
On the other hand,
Kuroki et al. have proposed an itinerant model based on
“pudding-mold” band structure, in which the difference in velocities of electrons and holes
is crucial [9]}.
Indeed, such a peculiar band shape is
observed by angle-resolved photoemission spectroscopy (ARPES) experiments [10]}, [11]}, [12]}, [13]}, [14]}
and
a large value of thermopower is calculated accordingly [15]}, [16]},
remaining the detailed conduction mechanism in this system controversial.
